Statistical Methods and Applications

, Volume 10, Issue 1–3, pp 157–174 | Cite as

A statistical model for orientation mechanism

  • Angela D'Elia
Statistical Applications

Abstract

A variance components model with response variable depending on both fixed effects of explanatory variables and random components is specified to model longitudinal circular data, in order to study the directional behaviour of small animals, as insects, crustaceans, amphipods, etc. Unknown parameter estimators are obtained using a simulated maximum likelihood approach. Issues concerning log-likelihood variability and the related problems in the optimization algorithm are also addressed. The procedure is applied to the analysis of directional choices under full natural conditions ofTalitrus saltator from Castiglione della Pescaia (Italy) beaches.

Key words

Circular data directional behaviour longitudinal data simulated maximum likelihood variance components 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramowitz M, Stegun IA (1965) Handbook of Mathematical Functions, New York: DoverGoogle Scholar
  2. Anderson CM, Jeff Wu CF (1996) Dispersion Measures and Analysis for Factorial Directional Data with Replicates, Applied Statistics,45, 47–61MATHCrossRefGoogle Scholar
  3. Breckling J (1989) The Analysis of Directional Time Series, Lecture Notes in Statistics 61. Berlin: Springer-VerlagMATHGoogle Scholar
  4. Coles SG (1998) Inference for Directional Distributions and Processes, Statistics and Computing8, 105–113CrossRefGoogle Scholar
  5. Cook RD, Weisberg S (1982) Residuals and Influence in Regression, New York: Chapman and HallMATHGoogle Scholar
  6. Diggle PJ (1990) Time Series: A Biostatistical Introduction. Oxford University Press: LondonGoogle Scholar
  7. Diggle PJ, Liang KY, Zeger SL (1994) Analysis of Longitudinal Data, Oxford: Clarendon PressMATHGoogle Scholar
  8. Fisher NI (1993) Statistical Analysis of Circular Data, Cambridge: Cambridge University PressMATHGoogle Scholar
  9. Fisher NI, Lee AJ (1983) A Correlation Coefficient for Circular Data, Biometrika70, 159–164MathSciNetGoogle Scholar
  10. Fisher NI, Lee AJ (1992) Regression Models for an Angular Response, Biometrics48, 665–677MathSciNetCrossRefGoogle Scholar
  11. Fisher NI, Lee AJ (1994) Time Series Analysis of Circular Data, Journal of the Royal Statistical Society B56, 327–339MATHMathSciNetGoogle Scholar
  12. Geyer CJ, Thompson EA (1992) Constrained Monte Carlo Maximum Likelihood for Dependent Data, (with discussion), Journal of the Royal Statistical Society54, 657–699MathSciNetGoogle Scholar
  13. Gould AL (1969) A Regression Technique for Angular Variates, Biometrics25, 683–700CrossRefGoogle Scholar
  14. Gouriéroux C, Monfort A (1996) Simulation-Based Econometric Methods, Oxford: Oxford University PressGoogle Scholar
  15. Johnson RA, Wehrly TE (1978) Some Angular-linear Distributions and Related Regression Models, Journal of the American Statistical Association73, 602–606MATHMathSciNetCrossRefGoogle Scholar
  16. Laird NM, Ware JH (1982) Random-effects Models for Longitudinal Data, Biometrics38, 963–974MATHCrossRefGoogle Scholar
  17. Liang KY, Zeger SL (1986) Longitudinal Data Analysis Using Generalized Linear Models, Biometrika73, 13–22MATHMathSciNetCrossRefGoogle Scholar
  18. Mardia KV (1972) Statistics of Directional Data, New York: Academic PressMATHGoogle Scholar
  19. Mardia KV, Jupp PE (2000) Directional Statistics, Chichester: John Wiley & SonsMATHGoogle Scholar
  20. Nelder JA, Mead R (1965) A Simplex Method for Function Minimization, The Computer Journal7, 308–313MATHGoogle Scholar
  21. Preisler HK, Akers RP (1995) Autoregressive-type Models for the Analysis of Bark Beetle Tracks, Biometrics51, 259–267CrossRefGoogle Scholar
  22. Presnell B, Morrison SP, Littell RC (1998) Projected Multivariate Linear Models for Directional Data, Journal of the American Statistical Association93, 1068–1077MATHMathSciNetCrossRefGoogle Scholar
  23. Ripley BD (1987) Stochastic Simulation, New York: WileyMATHGoogle Scholar
  24. Scapini F (1997) Variation in Scototaxis and Orientation Adaption of Talitrus saltator. Populations Subjected to Different Ecological Constraints Estuarine, Coastal and Shelf Science44, 139–146Google Scholar
  25. Smith DM, Robertson WH, Diggle PJ (1996) Oswald: Objected-Oriented Software for the Analysis of Longitudinal Data in S, Technical Report MA 96/192 Department of Mathematics and Statistics, University of Lancaster, UKGoogle Scholar
  26. Stiratelli R, Laird NM, Ware JH (1984) Random-effects Models for Serial Observations with Binary Response, Biometrics40, 961–971CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2001

Authors and Affiliations

  • Angela D'Elia
    • 1
  1. 1.Dipartimento di Scienze StatisticheUniversità di Napoli Federico IINapoliItaly

Personalised recommendations